Sur l'idéal du cône autocommutant des super algèbres de Lie basiques classiques et étranges
Cet article démontre que le cône de la partie impaire d’une super algèbre de Lie basique classique ou étrange défini par les équations est réduit.
Sur l'indice de certaines algèbres de Lie
On donne une majoration de l'indice de certaines algèbres de Lie introduites par V. Dergachev, A. Kirillov et D. Panyushev. On en déduit la preuve d'une conjecture de D. Panyushev. Nous formulons aussi une conjecture concernant l'indice de ces algèbres, et la prouvons dans des cas particuliers. Enfin, nous donnons un résultat concernant l'indice des sous-algèbres paraboliques d'une algèbre de Lie semi-simple.
Sur quelques théorèmes fondamentaux de l'algèbre moderne
Sur une algèbre Q-symétrique
We establish several properties of a quadratic algebra over a field k, which is a deformation of the symmetric algebra Sk³. In particular, we prove that A is an integral domain, noetherian and Koszul; we compute its first Hochschild cohomology group; we determine the corresponding Poisson structure on k³ and its symplectic leaves; we define an involution on A and describe the corresponding irreducible involutive representations.
Sur une famille d'algèbres de Lie idéalement finies
Surprising properties of centralisers in classical Lie algebras
Let be a classical Lie algebra, i.e., either , , or and let be a nilpotent element of . We study various properties of the centralisers . The first four sections deal with rather elementary questions, like the centre of , commuting varieties associated with , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on and symmetric invariants of .
Symmetric functions for the generating matrix of the Yangian of .
Symmetric Manifolds of Compact type Associated to the JB*-Triples Co (X,Z).
Symmetric quantum Weyl algebras
We study the symmetric powers of four algebras: -oscillator algebra, -Weyl algebra, -Weyl algebra and . We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.
Symmetries of an extended Hubbard Model
The Hamiltonian for an extended Hubbard model with phonons as introduced by A. Montorsi and M. Rasetti is considered on a D-dimensional lattice. The symmetries of the model are studied in various cases. It is shown that for a certain choice of the parameters a superconducting holds as a true quantum symmetry, but only for D=1.
Symmetries of the Kac-Peterson modular matrices of affine algebras.
Symmetry algebras and normal forms of third order ordinary differential equations.
Symplectic integrators to stochastic Hamiltonian dynamical systems derived from composition methods.
Symplectic K2 of Laurent polynomials, associated Kac-Moody groups and Witt rings.
Symplectic models of groups with noncommutative spaces
Symplectic structure in the enveloping algebra of a Lie algebra
Symplectic torus actions with coisotropic principal orbits
In this paper we completely classify symplectic actions of a torus on a compact connected symplectic manifold when some, hence every, principal orbit is a coisotropic submanifold of . That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manifold, of the torus action, or of the symplectic form.In order to deal with symplectic actions which are not Hamiltonian,...
Système de poids sur une algèbre de Lie nilpotente.
Systèmes de générateurs normalisants
Systèmes de racines infinis